Abstract: Robustness is one feature that sets organisms apart from engineered devices. Robustness has been defined, in part, as persistence - the ability to withstand perturbations in structure without change in function - and often includes concepts such as modularity, redundancy, self-repair, learning and adaptation. The use of exoskeletons in polypedal locomotion by arthropods represents an excellent system to examine robustness. Insects can still locomote with the loss of legs or damage to sensors. Cockroaches maintain their speed on hard surfaces and over rough terrain even after the loss of their feet. Cockroaches transition up a wall by colliding with it head-on at over one meter or 50 body lengths per second. These small animals rely on the robustness of their exoskeleton to simplify control. The rapid design of robust exoskeletons for small robots is now possible using a process called Smart Composite Microstructures. This approach enables the construction of small, strong, lightweight structures whose ability to move comes from bending of compliant polymer hinges that connect rigid links made from carbon fiber and other lightweight composites. These structures are made as single flat pieces that are folded to form more complicated shapes and linkages. This process has resulted in legged robots such as the 10 cm long, 16 g robot, DASH (Dynamic Autonomous Sprawled Hexapod Robot) that can sustain 8-story falls without damage and run away after a 10 meter per second impact. Moreover, rapid prototyping offers the possibility of designing legged robots as physical models to test biological hypotheses. A principled understanding of robustness remains a grand challenge for biology and a potential rich source of biological inspiration for engineering.